Year: 2026
Type: article
Abstract: The recently introduced random purification channel, which converts $n$ i.i.d. copies of any mixed quantum state into a uniform convex combination of $n$ i.i.d. copies of its purifications, has proved to be an extremely useful tool in quantum learning theory. Here we give a remarkably simple construction of this channel, making its known properties -- and several new ones -- immediately transparent. In particular, we show that the channel also purifies non-i.i.d. states: it transforms any permutationally symmetric state into a uniform convex combination of permutationally symmetric purifications, each differing only by a tensor-product unitary acting on the purifying system. We then apply the channel to give a one-line proof of (a stronger version of) the recently established Uhlmann's theorem for quantum divergences.
Source: Physical Review Letters
DOI: 10.1103/12p9-4krp
Authors: Filippo Girardi, Francesco Anna Mele, Ludovico Lami
Language: English
Subfield: Atomic and Molecular Physics, and Optics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
Funder: European Commission
Award: G2408725434
OpenAlex ID: W4416931824